Barry said it great.
For another picture on "stabilizing" think of a dried out corn cob. When stabilized, it is all corn cob with the voids filled with CA or other plasticized medium AND the corn cob's soft material itself is saturated and hardened. In this state, it is easy to turn.
Soft woods tear out real easily with scrapers or the skew when used in the scraper mode. By stabilizing the soft woods, they will be harder material and easier to turn.
A few woods will "bleed" over to - or "absorb" colors from other woods when two colors are glued to each other. Stabilized with CA or professionally - will help prevent or lessen this effect. This is probably the least used purpose of stabilizing but some try it on occasion.